Topological derivative and training neural networks for inverse problems

Authors:
Lidia Jackowska-Strumiłło;Jan Sokołowski;Antoni Zochowski
Affiliations:
Computer Engineering Department, Technical University of Łódz, Łódz, Poland;Institut Elie Cartan, Université Henri Poincaré, Vandoeuvre lès Nancy Cedex, France;Systems Research Institute of the Polish Academy of Sciences, Warszawa, Poland
Venue:
ICANN'05 Proceedings of the 15th international conference on Artificial neural networks: formal models and their applications - Volume Part II
Year:
2005

Citing 3
Cited 0

On the Topological Derivative in Shape Optimization

SIAM Journal on Control and Optimization
On Numerical Solution of Shape Inverse Problems

Computational Optimization and Applications
Optimality Conditions for Simultaneous Topology and Shape Optimization

SIAM Journal on Control and Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the problem of locating small openings inside the domain of definition of elliptic equation using as the observation data the values of finite number of integral functionals. Application of neural networks requires a great number of training sets. The approximation of these functionals by means of topological derivative allows to generate training data very quickly. The results of computations for 2D examples show, that the method allows to determine an approximation of the global solution to the inverse problem, sufficiently closed to the exact solution.